{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling and Simulation in Python\n",
    "\n",
    "Chapter 24\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "License: [Creative Commons Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import functions from the modsim.py module\n",
    "from modsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Rolling paper\n",
    "\n",
    "We'll start by loading the units we need."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "second"
      ],
      "text/latex": [
       "$\\mathrm{second}$"
      ],
      "text/plain": [
       "<Unit('second')>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "radian = UNITS.radian\n",
    "m = UNITS.meter\n",
    "s = UNITS.second"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And creating a `Params` object with the system parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Rmin</th>\n",
       "      <td>0.02 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rmax</th>\n",
       "      <td>0.055 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L</th>\n",
       "      <td>47 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>omega</th>\n",
       "      <td>10.0 radian / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>130 second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dt</th>\n",
       "      <td>1 second</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Rmin               0.02 meter\n",
       "Rmax              0.055 meter\n",
       "L                    47 meter\n",
       "omega    10.0 radian / second\n",
       "t_end              130 second\n",
       "dt                   1 second\n",
       "dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = Params(Rmin = 0.02 * m,\n",
    "                Rmax = 0.055 * m,\n",
    "                L = 47 * m,\n",
    "                omega = 10 * radian / s,\n",
    "                t_end = 130 * s,\n",
    "                dt = 1*s)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function estimates the parameter `k`, which is the increase in the radius of the roll for each radian of rotation. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_k(params):\n",
    "    \"\"\"Estimates the parameter `k`.\n",
    "    \n",
    "    params: Params with Rmin, Rmax, and L\n",
    "    \n",
    "    returns: k in meters per radian\n",
    "    \"\"\"\n",
    "    Rmin, Rmax, L = params.Rmin, params.Rmax, params.L\n",
    "    \n",
    "    Ravg = (Rmax + Rmin) / 2\n",
    "    Cavg = 2 * pi * Ravg\n",
    "    revs = L / Cavg\n",
    "    rads = 2 * pi * revs\n",
    "    k = (Rmax - Rmin) / rads\n",
    "    return k"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As usual, `make_system` takes a `Params` object and returns a `System` object."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def make_system(params):\n",
    "    \"\"\"Make a system object.\n",
    "    \n",
    "    params: Params with Rmin, Rmax, and L\n",
    "    \n",
    "    returns: System with init, k, and ts\n",
    "    \"\"\"\n",
    "    init = State(theta = 0 * radian,\n",
    "                 y = 0 * m,\n",
    "                 r = params.Rmin)\n",
    "    \n",
    "    k = estimate_k(params)\n",
    "\n",
    "    return System(params, init=init, k=k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing `make_system`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Rmin</th>\n",
       "      <td>0.02 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Rmax</th>\n",
       "      <td>0.055 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>L</th>\n",
       "      <td>47 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>omega</th>\n",
       "      <td>10.0 radian / second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>t_end</th>\n",
       "      <td>130 second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>dt</th>\n",
       "      <td>1 second</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>init</th>\n",
       "      <td>theta      0 radian\n",
       "y           0 meter\n",
       "r     ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>k</th>\n",
       "      <td>2.7925531914893616e-05 meter</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Rmin                                            0.02 meter\n",
       "Rmax                                           0.055 meter\n",
       "L                                                 47 meter\n",
       "omega                                 10.0 radian / second\n",
       "t_end                                           130 second\n",
       "dt                                                1 second\n",
       "init     theta      0 radian\n",
       "y           0 meter\n",
       "r     ...\n",
       "k                             2.7925531914893616e-05 meter\n",
       "dtype: object"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system = make_system(params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>theta</th>\n",
       "      <td>0 radian</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>r</th>\n",
       "      <td>0.02 meter</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "theta      0 radian\n",
       "y           0 meter\n",
       "r        0.02 meter\n",
       "dtype: object"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "system.init"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can write a slope function based on the differential equations\n",
    "\n",
    "$\\omega = \\frac{d\\theta}{dt} = 10$\n",
    "\n",
    "$\\frac{dy}{dt} = r \\frac{d\\theta}{dt}$\n",
    "\n",
    "$\\frac{dr}{dt} = k \\frac{d\\theta}{dt}$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def slope_func(state, t, system):\n",
    "    \"\"\"Computes the derivatives of the state variables.\n",
    "    \n",
    "    state: State object with theta, y, r\n",
    "    t: time\n",
    "    system: System object with r, k\n",
    "    \n",
    "    returns: sequence of derivatives\n",
    "    \"\"\"\n",
    "    theta, y, r = state\n",
    "    k, omega = system.k, system.omega\n",
    "    \n",
    "    dydt = r * omega\n",
    "    drdt = k * omega\n",
    "    \n",
    "    return omega, dydt, drdt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Testing `slope_func`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10.0 <Unit('radian / second')>,\n",
       " 0.2 <Unit('meter * radian / second')>,\n",
       " 0.0002792553191489362 <Unit('meter * radian / second')>)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "slope_func(system.init, 0, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll use an event function to stop when `y=L`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def event_func(state, t, system):\n",
    "    \"\"\"Detects when we've rolled length `L`.\n",
    "    \n",
    "    state: State object with theta, y, r\n",
    "    t: time\n",
    "    system: System object with L\n",
    "    \n",
    "    returns: difference between `y` and `L`\n",
    "    \"\"\"\n",
    "    theta, y, r = state\n",
    "    \n",
    "    return y - system.L"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "-47 meter"
      ],
      "text/latex": [
       "$-47\\ \\mathrm{meter}$"
      ],
      "text/plain": [
       "-47 <Unit('meter')>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "event_func(system.init, 0, system)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run the simulation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>success</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>message</th>\n",
       "      <td>A termination event occurred.</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "success                             True\n",
       "message    A termination event occurred.\n",
       "dtype: object"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results, details = run_ode_solver(system, slope_func, events=event_func)\n",
    "details"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And look at the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
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       "\n",
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       "\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>theta</th>\n",
       "      <th>y</th>\n",
       "      <th>r</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>122.00000</th>\n",
       "      <td>1220.0 radian</td>\n",
       "      <td>45.18218085106379 meter</td>\n",
       "      <td>0.05406914893617014 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>123.00000</th>\n",
       "      <td>1230.0 radian</td>\n",
       "      <td>45.72426861702124 meter</td>\n",
       "      <td>0.054348404255319074 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124.00000</th>\n",
       "      <td>1240.0 radian</td>\n",
       "      <td>46.269148936170176 meter</td>\n",
       "      <td>0.05462765957446801 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>125.00000</th>\n",
       "      <td>1250.0 radian</td>\n",
       "      <td>46.8168218085106 meter</td>\n",
       "      <td>0.054906914893616945 meter</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>125.33277</th>\n",
       "      <td>1253.3276965817133 radian</td>\n",
       "      <td>47.0 meter</td>\n",
       "      <td>0.054999842590712666 meter</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                               theta                         y  \\\n",
       "122.00000              1220.0 radian   45.18218085106379 meter   \n",
       "123.00000              1230.0 radian   45.72426861702124 meter   \n",
       "124.00000              1240.0 radian  46.269148936170176 meter   \n",
       "125.00000              1250.0 radian    46.8168218085106 meter   \n",
       "125.33277  1253.3276965817133 radian                47.0 meter   \n",
       "\n",
       "                                    r  \n",
       "122.00000   0.05406914893617014 meter  \n",
       "123.00000  0.054348404255319074 meter  \n",
       "124.00000   0.05462765957446801 meter  \n",
       "125.00000  0.054906914893616945 meter  \n",
       "125.33277  0.054999842590712666 meter  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.tail()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final value of `y` is 47 meters, as expected."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "47.0 meter"
      ],
      "text/latex": [
       "$47.0\\ \\mathrm{meter}$"
      ],
      "text/plain": [
       "47.0 <Unit('meter')>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "unrolled = get_last_value(results.y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The final value of radius is `R_max`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.054999842590712666 meter"
      ],
      "text/latex": [
       "$0.054999842590712666\\ \\mathrm{meter}$"
      ],
      "text/plain": [
       "0.054999842590712666 <Unit('meter')>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "radius = get_last_value(results.r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The total number of rotations is close to 200, which seems plausible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "199.47329822495885"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "radians = get_last_value(results.theta) \n",
    "rotations = magnitude(radians) / 2 / np.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The elapsed time is about 2 minutes, which is also plausible."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "125.33276965817134 second"
      ],
      "text/latex": [
       "$125.33276965817134\\ \\mathrm{second}$"
      ],
      "text/plain": [
       "125.33276965817134 <Unit('second')>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_final = get_last_label(results) * s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting `theta`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_theta(results):\n",
    "    plot(results.theta, color='C0', label='theta')\n",
    "    decorate(xlabel='Time (s)',\n",
    "             ylabel='Angle (rad)')\n",
    "    \n",
    "plot_theta(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting `y`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_y(results):\n",
    "    plot(results.y, color='C1', label='y')\n",
    "\n",
    "    decorate(xlabel='Time (s)',\n",
    "             ylabel='Length (m)')\n",
    "    \n",
    "plot_y(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting `r`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_r(results):\n",
    "    plot(results.r, color='C2', label='r')\n",
    "\n",
    "    decorate(xlabel='Time (s)',\n",
    "             ylabel='Radius (m)')\n",
    "    \n",
    "plot_r(results)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also see the relationship between `y` and `r`, which I derive analytically in the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(results.r, results.y, color='C3')\n",
    "\n",
    "decorate(xlabel='Radius (m)',\n",
    "         ylabel='Length (m)',\n",
    "         legend=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's the figure from the book."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Saving figure to file figs/chap24-fig01.pdf\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_three(results):\n",
    "    subplot(3, 1, 1)\n",
    "    plot_theta(results)\n",
    "\n",
    "    subplot(3, 1, 2)\n",
    "    plot_y(results)\n",
    "\n",
    "    subplot(3, 1, 3)\n",
    "    plot_r(results)\n",
    "\n",
    "plot_three(results)\n",
    "savefig('figs/chap24-fig01.pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Animation\n",
    "\n",
    "Here's a draw function that animates the results using `matplotlib` patches."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib.patches import Circle\n",
    "from matplotlib.patches import Arrow\n",
    "\n",
    "def draw_func(state, t):\n",
    "    # get radius in mm\n",
    "    theta, y, r = state\n",
    "    radius = r.magnitude * 1000\n",
    "    \n",
    "    # draw a circle with\n",
    "    circle = Circle([0, 0], radius, fill=True)\n",
    "    plt.gca().add_patch(circle)\n",
    "    \n",
    "    # draw an arrow to show rotation\n",
    "    dx, dy = pol2cart(theta, radius)\n",
    "    arrow = Arrow(0, 0, dx, dy)\n",
    "    plt.gca().add_patch(arrow)\n",
    "\n",
    "    # make the aspect ratio 1\n",
    "    plt.axis('equal')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "animate(results, draw_func)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Run the simulation again with a smaller step size to smooth out the animation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercises\n",
    "\n",
    "**Exercise:** Since we keep `omega` constant, the linear velocity of the paper increases with radius.  Use `gradient` to estimate the derivative of `results.y`.  What is the peak linear velocity?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "dydt = gradient(results.y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(dydt, label='dydt')\n",
    "decorate(xlabel='Time (s)',\n",
    "         ylabel='Linear velocity (m/s)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.5504654255319086 meter/second"
      ],
      "text/latex": [
       "$0.5504654255319086\\ \\frac{\\mathrm{meter}}{\\mathrm{second}}$"
      ],
      "text/plain": [
       "0.5504654255319086 <Unit('meter / second')>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "linear_velocity = get_last_value(dydt) * m/s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose the peak velocity is the limit; that is, we can't move the paper any faster than that.\n",
    "\n",
    "Nevertheless, we might be able to speed up the process by keeping the linear velocity at the maximum all the time.\n",
    "\n",
    "Write a slope function that keeps the linear velocity, `dydt`, constant, and computes the angular velocity, `omega`, accordingly.\n",
    "\n",
    "Run the simulation and see how much faster we could finish rolling the paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "def slope_func(state, t, system):\n",
    "    \"\"\"Computes the derivatives of the state variables.\n",
    "    \n",
    "    state: State object with theta, y, r\n",
    "    t: time\n",
    "    system: System object with r, k\n",
    "    \n",
    "    returns: sequence of derivatives\n",
    "    \"\"\"\n",
    "    theta, y, r = state\n",
    "    k, omega = system.k, system.omega\n",
    "    \n",
    "    dydt = linear_velocity\n",
    "    omega = dydt / r\n",
    "    drdt = k * omega\n",
    "    \n",
    "    return omega, dydt, drdt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(27.523271276595427 <Unit('1 / second')>,\n",
       " 0.5504654255319086 <Unit('meter / second')>,\n",
       " 0.0007686019904368403 <Unit('meter / second')>)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "slope_func(system.init, 0, system)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>success</th>\n",
       "      <td>True</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>message</th>\n",
       "      <td>A termination event occurred.</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "success                             True\n",
       "message    A termination event occurred.\n",
       "dtype: object"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "results, details = run_ode_solver(system, slope_func, events=event_func)\n",
    "details"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "85.38229254741002 second"
      ],
      "text/latex": [
       "$85.38229254741002\\ \\mathrm{second}$"
      ],
      "text/plain": [
       "85.38229254741002 <Unit('second')>"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "t_final = get_last_label(results) * s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x720 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "plot_three(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
